PORTFOLIO OPTIMIZATION UNDER CARDINALITY CONSTRAINTS: A METAHEURISTIC MEAN-VARIANCE APPROACH

Juwita Nur Ihzza; Noviyanti Santoso; Moch Abdillah Nafis

doi:10.22437/jiituj.v10i2.53849

Authors

Juwita Nur Ihzza Institut Teknologi Sepuluh Nopember
Noviyanti Santoso https://orcid.org/0000-0002-8139-8676
Moch Abdillah Nafis Institut Teknologi Sepuluh Nopember https://orcid.org/0000-0001-5319-5970

DOI:

https://doi.org/10.22437/jiituj.v10i2.53849

Keywords:

Artificial Bee Colony, Cardinality Constrained Mean Variance, Metaheuristic, Particle Swarm Optimization

Abstract

The growing emphasis on sustainability in investment decisions necessitates portfolio optimization models that incorporate practical constraints, particularly asset cardinality. This study applies a Cardinality-Constrained Mean–Variance (CCMV) framework, which increases computational complexity due to the limited number of selected assets. To address this, two metaheuristic algorithms, namely Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC) are implemented. Using data from 25 stocks observed between March and August 2025, the analysis includes asset screening based on the risk-free rate, portfolio optimization, and performance evaluation using expected return, risk, and the Sharpe ratio. PSO produces an optimal portfolio of 8 assets with a Sharpe ratio of 27.594%, while ABC selects 9 assets and achieves a slightly higher Sharpe ratio of 27.599%. Although the difference is marginal, ABC demonstrates superior computational efficiency. The findings highlight the effectiveness of metaheuristic approaches, particularly ABC, in solving constrained portfolio optimization problems.

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Author Biographies

Juwita Nur Ihzza, Institut Teknologi Sepuluh Nopember

Department of Business Statistics, Institut Teknologi Sepuluh Nopember, Jawa Timur, Indonesia

Noviyanti Santoso

Department of Business Statistics, Institut Teknologi Sepuluh Nopember, Jawa Timur, Indonesia

Moch Abdillah Nafis, Institut Teknologi Sepuluh Nopember

Department of Business Statistics, Institut Teknologi Sepuluh Nopember, Jawa Timur, Indonesia

References

Ahmed, F., & Chowdhury, M. A. R. (2024). Capital Market Efficiency and Economic Growth: Evidence from Bangladesh. European Journal of Development Studies, 4(2), 1–6. https://doi.org/10.24018/ejdevelop.2024.4.2.343.

Arouri, M., Mhadhbi, M., & Shahrour, M. H. (2025). Dynamic Connectedness and Hedging Effectiveness Between Green Bonds, ESG Indices, and Traditional Assets. European Financial Management, 31(5), 1704–1719. https://doi.org/10.1111/eufm.12561.

Bagh, T., Hunjra, A. I., Ntim, C. G., & Naseer, M. M. (2025). Capitalizing on risk: How corporate financial flexibility, investment efficiency, and institutional ownership shape risk-taking dynamics. International Review of Economics & Finance, 99, 104068. https://doi.org/10.1016/j.iref.2025.104068.

Chang, T.-J., Meade, N., Beasley, J. E., & Sharaiha, Y. M. (2000). Heuristics for cardinality constrained portfolio optimisation. Computers & Operations Research, 27(13), 1271–1302. https://doi.org/10.1016/S0305-0548(99)00074-X.

Chen, A. H. L., Liang, Y.-C., & Liu, C.-C. (2012). An artificial bee colony algorithm for the cardinality-constrained portfolio optimization problems. 2012 IEEE Congress on Evolutionary Computation, 1–8. https://doi.org/10.1109/CEC.2012.6252920.

Cura, T. (2009). Particle swarm optimization approach to portfolio optimization. Nonlinear Analysis: Real World Applications, 10(4), 2396–2406. https://doi.org/10.1016/j.nonrwa.2008.04.023.

Dash, S. S., Nayak, S. K., & Mishra, D. (2021). ABC Versus PSO: A Comparative Study and Analysis on Optimization Aptitude (pp. 527–544). https://doi.org/10.1007/978-981-16-0695-3_50.

Eom, C., Kaizoji, T., Livan, G., & Scalas, E. (2021). Limitations of portfolio diversification through fat tails of the return Distributions: Some empirical evidence. The North American Journal of Economics and Finance, 56, 101358. https://doi.org/10.1016/j.najef.2020.101358.

Febrianti, W., Sidarto, K. A., & Sumarti, N. (2022). Solving Constrained Mean-Variance Portfolio Optimization Problems Using Spiral Optimization Algorithm. International Journal of Financial Studies, 11(1), 1. https://doi.org/10.3390/ijfs11010001.

Fu, L., Li, J., & Pu, S. (2023). A comparative study of heuristic methods for cardinality constrained portfolio optimization. High-Confidence Computing, 3(1), 100097. https://doi.org/10.1016/j.hcc.2022.100097.

Gasmara, D. D., Achsani, N. A., & Bandono, B. (2023). Optimization investment portfolio of ESG capital market in Indonesia: An investigation of Polynomial Goal Programming based on higher moments. Jurnal Ekonomi Dan Bisnis, 26(2), 477–492. https://doi.org/10.24914/jeb.v26i2.9666.

González-Bueno, J., Tamošiūnienė, R., Gómez Morales, C., & Rueda-Barrios, G. (2025). Applying the mean-variance framework: portfolio optimization and comparative performance analysis in the emerging Colombian capital market. Business, Management and Economics Engineering, 23(01), 164–188. https://doi.org/10.3846/bmee.2025.22695.

Kalayci, C. B., Ertenlice, O., & Akbay, M. A. (2019). A comprehensive review of deterministic models and applications for mean-variance portfolio optimization. Expert Systems with Applications, 125, 345–368. https://doi.org/10.1016/j.eswa.2019.02.011.

Karaboga, D. (2005). An idea based on honey bee swarm for numerical optimization. 1–10.

Kennedy, J., & Eberhart, R. (n.d.). Particle swarm optimization. Proceedings of ICNN’95 - International Conference on Neural Networks, 1942–1948. https://doi.org/10.1109/ICNN.1995.488968.

Kulkarni, V. R., & Desai, V. (2016). ABC and PSO: A comparative analysis. 2016 IEEE International Conference on Computational Intelligence and Computing Research (ICCIC), 1–7. https://doi.org/10.1109/ICCIC.2016.7919625.

Mansouri, T., & Moghadam, M. R. S. (2021). Markowitz-based cardinality constrained portfolio selection using Asexual Reproduction Optimization (ARO).

Markowitz, H. (1952). PORTFOLIO SELECTION*. The Journal of Finance, 7(1), 77–91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x.

Müller, L., & Joubrel, M. (2025). A novel approach to sustainable mean-variance portfolio optimization: Accounting for ESG-related uncertainty. Finance Research Letters, 85, 108056. https://doi.org/10.1016/j.frl.2025.108056.

Pires, G., Wanke, P., Antunes, J., Tan, Y., & Tzeremes, N. G. (2026). Portfolio optimization with minimum assets and dividend yield constraints. Annals of Operations Research. https://doi.org/10.1007/s10479-026-07084-2.

Priyadarshi, R., & Kumar, R. R. (2025). Evolution of Swarm Intelligence: A Systematic Review of Particle Swarm and Ant Colony Optimization Approaches in Modern Research. Archives of Computational Methods in Engineering, 32(6), 3609–3650. https://doi.org/10.1007/s11831-025-10247-2.

Taheripour, E., Sadjadi, S. J., & Amiri, B. (2025). A multi-criteria approach to ESG-based portfolio optimization incorporating historical performance, forward-looking insights, and credibilistic CVaR: a case study on the DJIA. Scientific Reports, 15(1), 39088. https://doi.org/10.1038/s41598-025-24242-x.

The Effectiveness of Different Portfolio Diversification Strategies on Reducing Risk: A Survey Based on Financial Advisors (2021). (2023). Journalofcardiovasculardiseaseresearch, 12(06). https://doi.org/10.48047/jcdr.2021.12.06.328.

Wang, H. (2025). A Risk-Return Comparison Study of ESG Portfolios and Traditional Portfolios. Advances in Economics, Management and Political Sciences, 174(1), 14–19. https://doi.org/10.54254/2754-1169/2025.21833.

Yaman, S., & Tuncel, M. B. (2025). The benefits of sectoral diversification for investors with different risk perceptions. Borsa Istanbul Review, 25(3), 597–616. https://doi.org/10.1016/j.bir.2025.02.008.